By the time the first episode of Berikyuu airs, Mano Erina will have graduated the Eggs. So technically it is not "Berryz, C-ute featuring an Egg", but that is just a detail.
MoroP (the producer) said in his blog there will be many H!P members as guests on the show. That could include Eggs, but are they official H!P members? I think we'll see more of the popular H!P members at first anyway.